Question: Simplify the following expression and state the condition under which the simplification is valid: $a = \dfrac{z^2 - z}{z^2 + 2z - 3}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{z^2 - z}{z^2 + 2z - 3} = \dfrac{(z)(z - 1)}{(z + 3)(z - 1)} $ Notice that the term $(z - 1)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(z - 1)$ gives: $a = \dfrac{z}{z + 3}$ Since we divided by $(z - 1)$, $z \neq 1$. $a = \dfrac{z}{z + 3}; \space z \neq 1$